The Complexity of the Core Model

Ulam序列算术复杂性与绝对刚性现象

Arithmetical Complexity and Absoluteness of Rigidity Phenomena for Ulam Sequences

本文研究Ulam序列的算术复杂性与绝对刚性现象，证明相关陈述在算术层级中处于低层，并在不同模型间具有绝对性。

Absolutely Choiceless Proofs

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice holds and use absoluteness. We examine the complexity of the sentences that this technique can be applied to, and show that many of the theorems in basic partition calculus have the adequate complexity for this technique to apply.

迈向Chang模型的泛型绝对性定理

Towards a generic absoluteness theorem for Chang models

本文引入新方法建立含所有普遍贝尔实数集的模型的泛型绝对性结果，基于超紧基数等假设证明相关导出模型性质，还得出可定义幂集等结构的理论无法被力迫改变的结论。